Returning home to live with your parents might not be as big a cost saver as you think — at least when it comes to auto insurance.

Millennials who are living at home with their parents pay up to 73 percent more for auto insurance than people their age who own a home, according to new research from auto insurance comparison site Compare.com. Those so-called "boomerang kids" are shelling out an average $1,750 per year on premiums, versus averages of $1,205 for those who own a single family home and $1,009 for those who own a condo.

Compare.com's research came from data the company gathered on 2.3 million American drivers who used the site to obtain auto insurance quotes.

What's behind the gap?

Risk factors that insurers consider include age, type of car, zip code and driving record, among others, said Andrew Rose, chief executive of Compare.com — so millennials already tend to be more vulnerable than other generations in those assessments due to their relative lack of experience with driving and credit. Owning a home can reduce rates because the insurer has more evidence of financial responsibility, he said.

Millennials who don't own a home are missing out on the potential of bundling discounts for combining auto and home insurance under the same carrier.

However, millennials assessing their auto insurance should take those average premiums with a grain of salt. Of the consumer quotes Compare.com analyzed, half came from just three states: Georgia, Texas and California.

Major metropolitan areas in those states have "legendary gridlock," and are likelier as a whole to face higher auto insurance premiums, said Lynne McChristian, a spokesperson for the Insurance Information Institute.

"The single best way to lower auto insurance rates is to shop," Rose said in an interview with CNBC.

Quotes from multiple carriers can differ by up to a $1,500, he said, and this diligent shopping can save drivers more than $50,000 over a lifetime.

Rose said that in many cases, millennials living at home can pay less for insurance if they remain on their parents' plans. But insurance companies often want drivers in their 20's to have their own policies, so that strategy may not be an option even if your parents are willing.

As soon as you move out on your own, car insurance is one of the first expenses to revisit, Rose said. It's a smart move even if you don't buy a home: auto premiums vary by zip code, so your new locale may offer cheaper rates.

"You should stock the fridge with beer and pizza, and then shop your auto insurance," he said.